roberto plans to use two transformers to reduce a voltage of 120 v to 4 v. he uses a transformer that has…
roberto plans to use two transformers to reduce a voltage of 120 v to 4 v. he uses a transformer that has 300 coils in the primary winding and 50 coils in the secondary winding. he has four other transformers, as listed in the table.\n\n| transformer | primary winding (coils) | secondary winding (coils) |\n| ---- | ---- | ---- |\n| w | 80 | 20 |\n| x | 60 | 12 |\n| y | 70 | 35 |\n| z | 50 | 5 |\n\nwhich transformer should roberto use to have an ending voltage of 4 v?\no w\no x\no y\no z
Answer
Explanation:
Step1: Calculate the output voltage of the first - stage transformer
The voltage - transformation ratio for a transformer is given by $\frac{V_p}{V_s}=\frac{N_p}{N_s}$, where $V_p$ is the primary voltage, $V_s$ is the secondary voltage, $N_p$ is the number of primary coils, and $N_s$ is the number of secondary coils. For the first transformer with $N_{p1}=300$ and $N_{s1}=50$ and $V_{p1}=120$ V, we have $\frac{V_{p1}}{V_{s1}}=\frac{N_{p1}}{N_{s1}}$. So $V_{s1}=\frac{N_{s1}}{N_{p1}}\times V_{p1}=\frac{50}{300}\times120 = 20$ V.
Step2: Calculate the required transformation ratio for the second - stage transformer
We want the final output voltage $V_{s2}=4$ V. Since the input voltage to the second - stage transformer is $V_{p2}=V_{s1} = 20$ V, the required transformation ratio for the second - stage transformer is $\frac{V_{p2}}{V_{s2}}=\frac{20}{4}=5$.
Step3: Check the transformation ratio of each given transformer
For transformer W: $\frac{N_{pW}}{N_{sW}}=\frac{80}{20}=4$. For transformer X: $\frac{N_{pX}}{N_{sX}}=\frac{60}{12}=5$. For transformer Y: $\frac{N_{pY}}{N_{sY}}=\frac{70}{35}=2$. For transformer Z: $\frac{N_{pZ}}{N_{sZ}}=\frac{50}{5}=10$.
Answer:
X